Question

Two vessels separately contain two ideal gases $A$ and $B$ at the same temperature. The pressure of $A$ being twice that of $B$. Under such conditions, the density of $A$ is found to be $1.5$ times the density of $B$. The ratio of molecular weight of $A$ and $B$ is

• A. $3/4$
• B. $2$
• C. $1/2$
• D. $2/3$

Answer 1

The correct option is A $3/4$

Given,

$P_A:P_B=2:1$

${\rho }_A:{\rho }_B=3:2$

The ideal gas equation,

$PV=nRT$

$P=\frac{\rho }{M}RT$

$M=\frac{\rho }{P}RT$. . . . .(1)

From equation (1), The molecular weight depends on density and Pressure.

$M\alpha \frac{\rho }{P}$

so, $\frac{M_A}{M_B}=\frac{P_B{\rho }_A}{P_A{\rho }_B}$

$\frac{M_A}{M_B}=\frac{1}{2}\times \frac{3}{2}=\frac{3}{4}$

$M_A:M_B=3:4$

The correct option is A.